"always getting into fights" is no experience at all.
and dont run before you can jump.
theres along old amature route you should try before you even think about professionally and certainly just a class or two wont cut it!

as for your age, of course its not too late.
i only wish i had got involved in mma as early as 19, (im 38 now, and yes still doing mma)

why would you wish to do a class in various martial arts? the whole idea of a mma class is that they will work on all the areas, thats why its called mixed, lol.
find a class that suits what you want to do.
if its fighting in the cage, then your looking for an mma class that will cover standup, clinch and groundwork.

get enrolled, show them what you think you got, and they will show you what you havent got...
have fun!